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# statistics

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Behavior Entertainment put out a new gaming mechanic that 70% of all other gaming developers report that will bring in a new surge of players. If 10 new players take part in the new mechanic, find the probability that five will stick with the new gaming mechanic.

Mar 15, 2023

#1
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We can solve this problem using the binomial distribution. Let X be the number of new players who stick with the new gaming mechanic, and let p be the probability that a new player sticks with the new gaming mechanic. Since 70% of all other gaming developers report that the new gaming mechanic will bring in a new surge of players, we have:

p = 0.7

We want to find the probability that five new players stick with the new gaming mechanic, so we have:

X ~ Binomial(n = 10, p = 0.7)

P(X = 5) = (10 choose 5) * (0.7)^5 * (1 - 0.7)^(10 - 5)

Using the formula for the binomial coefficient, we can simplify the expression as:

P(X = 5) = (10! / (5! * (10 - 5)!)) * (0.7)^5 * (0.3)^5

Simplifying further, we get:

P(X = 5) = 252 * 0.16807 * 0.00243

P(X = 5) = 0.102

Therefore, the probability that five new players will stick with the new gaming mechanic is approximately 0.102 or 10.2%.

Mar 15, 2023
#2
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If I understand the question correctly

10C5  *  0.7^5 * 0.3^5 = approx 10.29 %

Mar 15, 2023